In arm A, RO6839921 will be given to patients with advanced solid tumor malignancies. In Arm B, RO6839921 will be given to patients with relapsed/refractory acute myeloid leukemia (AML). The arms will escalate independently. Escalation will begin in solid tumor patients (Arm A) in single patient cohorts, using a new Continual Reassessment Method (n-CRM). Escalation for AML patients will be initiated at or below the dose level that causes >/= Grade 2 hematologic side effects in Arm A. Escalation in AML patients will follow a rolling 6 design.